Abstract The variational theory of higher-power energy is developed for mappings between Riemannian manifolds, and more generally sections submersions applied to vector bundles their sphere subbundles. A complete classification then given left-invariant fields on three-dimensional unimodular Lie groups equipped with an arbitrary metric.

Dedicated to Professor WeiYue Ding on the occasion of his 60th birthday Abstract For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable-stationary harmonic maps to the sphere S. We show that the singular set of stable-stationary harmonic maps from B to S is the union of finitely many isolated singular points and finitely many Hölder continuous curves. We also...

In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds B and F into the doubly warped product f B ×b F can not be proper biharmonic maps. Also we analyze the conditions for the biharmonicity of projections f B ×b F → B and f B ×b F → F , respectively. Some characterizations for non-harmonic biharmonic maps are g...

We discuss recent progress in the study of the space of harmonic maps from the 2sphere to the unit n-sphere in Euclidean (n+1)-space. We consider the structure of this space as an algebraic variety, the existence of non-manifold points in this space, and the relation between this question and the integrability of Jacobi fields along harmonic maps. One of the main tools used is that of the twist...

We study in this paper harmonic maps and harmonic morphisms on Kenmotsu manifolds. We also give some results on the spectral theory of a harmonic map for which the target manifold is a Kenmotsu manifold.